Pair of Linear Equations in Two Variables — Question Ex 3.7 Q6
Back to all questionsEx 3.7 Class 10 Maths Question 6.
Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the coordinates of the vertices of the triangle formed by these lines and the y-axis.
5x – y = 5 …(i)
3x-y = 3 …(ii)
For graphical representation:
From equation (i), we get: y = 5x – 5
When x = 0, then y -5
When x = 2, then y = 10 – 5 = 5
When x = 1, then y = 5 – 5 = 10
Thus, we have the following table of solutions:
From equation (ii), we get:
⇒ y = 3x – 3
When x = 0, then y = -3
When x = 2, then y = 6 – 3 = 3
When x = 1, then y = 3 – 3 = 0
Thus, we have the following table of solutions:
Plotting the points of each table of solutions, we obtain the graphs of two lines intersecting each other at a point C(1, 0).
The vertices of ΔABC formed by these lines and the y-axis are A(0, -5), B(0, -3) and C(1, 0).
CBSE Class 10 Pair of Linear Equations — Complete Guide
This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.
Quick Revision: Key Concepts
- Unique solution: a1/a2 ≠ b1/b2 (intersecting lines)
- Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
- No solution: a1/a2 = b1/b2 ≠ c1/c2 (parallel lines)
- Methods: Substitution, Elimination, Cross-multiplication
- Reducible equations: Substitute u = 1/x, v = 1/y
Most Important Questions
- Determine consistency of a system of equations
- Solve using elimination or substitution method
- Word problems: age, speed, fraction, geometry type
- Equations reducible to linear form (1/x, 1/y type)
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